Masud BehniaSchool of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia

Abstract

Im some previous investigations it has been shown that existing laws for the boundary layer thickness, velocity and time to steady state for the natural convection flow over an evenly heated plate provide a very poor prediction of the Prandtl number dependency of the flow, while providing a good prediction of the Rayleigh number dependency. The primary failing of the existing scaling, for Prandtl numbers greater than 1.0, is that the boundary layer model used does not fully represent a fluid with a finite Prandtl number. A new Prandtl number scaling has been developed using a triple-layer integral approach. Comparison to direct numerical simulation and semi-analytic results show that this scaling performs considerably better than the previous scaling, providing a good representation of both the velocity maximum and the internal structure of the boundary layer. The scaling derivation and comparisons with direct numerical simulations and semi-analytic results are presented.